Fano resonance based optical modulator reaching 85% modulation depthWenyu Zhao, Huan Jiang, Bingyi Liu, Yongyuan Jiang, Chengchun Tang, and Junjie Li Citation: Applied Physics Letters 107, 171109 (2015); doi: 10.1063/1.4935031 View online: http://dx.doi.org/10.1063/1.4935031 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/107/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Enhancement of light absorption using high-k dielectric in localized surface plasmon resonance for silicon-basedthin film solar cells J. Appl. Phys. 109, 093516 (2011); 10.1063/1.3587165 Fully complementary metal-oxide-semiconductor compatible nanoplasmonic slot waveguides for siliconelectronic photonic integrated circuits Appl. Phys. Lett. 98, 021107 (2011); 10.1063/1.3537964 Far-field observation of the radial profile of visible whispering-gallery modes in a single microdisk based on Si-nanocrystal/ Si O 2 superlattices J. Appl. Phys. 106, 123102 (2009); 10.1063/1.3273360 Resonance control of membrane reflectors with effective index engineering Appl. Phys. Lett. 95, 023110 (2009); 10.1063/1.3182801 Tunable optical filters with nanostructured suspended gratings J. Vac. Sci. Technol. B 27, 1035 (2009); 10.1116/1.3114465

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Fano resonance based optical modulator reaching 85% modulation depth

Wenyu Zhao,1 Huan Jiang,1 Bingyi Liu,1 Yongyuan Jiang,1,2,a) Chengchun Tang,3

and Junjie Li31Department of Physics, Harbin Institute of Technology, Harbin 150001, China2Key Laboratory of Micro-Optics and Photonic Technology of Heilongjiang Province, Harbin 150001, China3Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academyof Sciences, P.O. Box 603, Beijing 100190, China

(Received 7 September 2015; accepted 21 October 2015; published online 29 October 2015)

In this paper, we demonstrate the combination of nematic liquid crystal with a binary silicon nanohole

array to realize a high performance Fano resonance based optical modulator. The simulations using a

finite difference time domain method reveal that the sharp Fano profile in the binary array originates

from the interaction of the in-phased and anti-phased lattice collective resonance hybridized through

lattice coupling effects. Experimental results agree very well with the simulations and demonstrate the

strong dependence of the Q factor and spectral contrast of the resonance on the radius difference of the

two nanohole arrays. Infiltrated with nematic liquid crystal, E7, the Fano profile can be dynamically

and continuously tuned by an applied voltage, and an unprecedented modulation depth up to 85% is

achieved. VC 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4935031]

Active plasmonics enabling real-time control over nano-

devices’ properties have attracted a tremendous amount of

attention in the past few years.1–4 Great progress has been

made towards a wealth of promising applications such as

active catalysis,5 optical nanoantennas,6 solar cells,7 and bio-

logical sensing and imaging.8 Among the various active tun-

ing media, such as stimuli-responsive polymers,9

photochromic molecules10 and inorganic phase-transition

materials,11 liquid crystal (LC) is an excellent candidate

because of its relatively large birefringence on refractive

index and versatile driven methods to stimulate molecule

realignment.1,2 Many research works have been conducted to

incorporate the LC into metal nanostructures to manipulate

the transmission or the reflection of the plasmonic structures,

which have potentials for color filters, nano-switches, and

nano-modulators.12–19 However, due to the low Q factor and

poor spectral contrast of the resonances in metal nanostruc-

tures, the modulation depths underpinning most nano-

devices are limited to rather small values posing a great

obstacle for practical applications. Improving the perform-

ance of modulation depth remains a major challenge and

more research efforts are desirable.

Recently, Fano resonances in nanostructures resulting

from the interaction of “dark states” and “bright states” have

been extensively studied.20,21 Due to the high Q factor and

spectral contrast, Fano resonances have been employed in

many applications where sharp resonances are essential for

the performances such as biosensors,22 filters,23 surface-

enhanced Raman scattering (SERS),24 and surface plasmon

lasers.25 More recently, we demonstrated a binary silicon

particle array and studied the multi-trapped modes and corre-

sponding Fano resonances resulting from the lattice coupling

effects in the array.26 Because of the low loss nature of

dielectric,27–29 the Q factor and spectral contrast of such

Fano resonances can be strongly improved simultaneously

resulting in an ultra-high figure of merit that is orders higher

than its conventional counterparts made of metal.

In this paper, we take advantage of the easy tuning mecha-

nism of nematic LC and the high Q factor and spectral contrast

of the Fano resonance in a binary nanohole array perforated in

a silicon film to realize a high performance optical modulator.

Simulations using finite difference time domain method dem-

onstrate that the origin of the sharp asymmetric profile sup-

ported by the binary nanohole array is related to the excitations

of the anti-phased lattice collective resonance (ALCR) and the

in-phased lattice collective resonance (ILCR) hybridized

through lattice coupling effects. Experimental results and sim-

ulations are in very good agreement and show the strong de-

pendence of the Q factor and spectral contrast on the radius

difference between the two nanohole arrays. We then incorpo-

rate commercial E7 LC into the binary nanohole array and

study the performance of such structure as optical modulator.

The Fano profile dynamically shifts towards the short wave-

length as the applied voltage gradually increases from 0 to

26.7 kV/cm, and modulation depth up to 85% can be realized

for the operating wavelength of 713 nm.

Fig. 1(a) shows the artistic impression of the binary nano-

hole array composed of two nanohole arrays with different

radii of R1 and R2 perforated in a silicon film (H ¼ 30 nm).

The periods of the two arrays are both P (400 nm) and the

centers of the nanoholes have a displacement of half period.

In order to fabricate the binary nanohole array, a layer of

amorphous silicon film is deposited using plasma enhanced

chemical vapor deposition (PECVD) method on a glass sub-

strate pre-deposited an indium tin oxide (ITO) layer of 20 nm

as electrode. The binary nanohole arrays with footprints of

100 lm� 100 lm are then fabricated using standard electron

beam lithography followed by ion beam etching process

(Fig. 1(c)). To measure the transmission of the samples, white

light from a halogen tungsten lamp is focused on a spot size

of nearly 50 lm in diameter by a 5� objective, and then on

the other side collected by another 20� objective and trans-

mitted to an optical fiber spectrometer (USB2000þ, Ocean

a)Author to whom correspondence should be addressed. Electronic mail:

jiangyy@hit.edu.cn

0003-6951/2015/107(17)/171109/5/$30.00 VC 2015 AIP Publishing LLC107, 171109-1

APPLIED PHYSICS LETTERS 107, 171109 (2015)

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Optics). The simulations are conducted using commercial

finite difference time domain method software, FDTD

Solutions from Lumerical, Inc. The permittivity of glass, sili-

con, and ITO are extracted from the experimental data.30,31

A sharp Fano resonance with a high spectral contrast

(Fig. 1(b)) appears in transmission around 650 nm, and the

Fano profile evolves from a dip of 4% transmission to a peak

of 65% transmission within 10 nm. Measured transmission

(Fig. 1(d)) agrees very well with the simulation results except

a slight deviation of resonance wavelength mainly due to the

deviations of geometric parameters caused during fabrication

process. The distinct Fano profile can be explained using the

hybridization theory;26 each nanohole array supports corre-

sponding lattice collective resonance which is the lattice col-

lective excitations of the cavity modes supported by the

constituent nanoholes in the array.32 When two nanohole

arrays with different radii are combined to form a binary one,

the two supported lattice collective resonance modes with dif-

ferent resonant energies will hybridize to generate the ILCR

mode and ALCR mode through lattice coupling effects. In the

ILCR mode, two nanohole arrays will always oscillate

towards the same direction either in-phase or anti-phase with

the incident light; thus, the reradiated fields of the two nano-

hole arrays interfere constructively in the far field resulting in

an enhanced radiation to the free space. The ILCR mode is

termed as “bright mode” because of its enhanced scattering

and effective coupling to the incident light. In the ALCR

mode, two arrays will oscillate towards the opposite direc-

tions, leading to the destructive reradiated fields in the far field

and strong elimination of scattering loss. This resonant mode

can be considered the “dark mode” due to its long lifetime

and weak coupling to the free space radiation. The interaction

of the ALCR mode and ILCR mode gives rise to the sharp

asymmetric Fano profile in transmission.

To interpret the ALCR mode and ILCR mode more

clearly, we plot the phase map of the electric field of the bi-

nary array for a unit cell at the plane across the centers of

each nanohole (Z¼ 15 nm). Figs. 2(a) and 2(b) correspond to

the phase map at 660 nm and 740 nm (R1 ¼ 50 nm and

R2 ¼ 110 nm), respectively. The excited cavity modes in the

FIG. 1. (a) Artistic impression of binary silicon nanohole array with different

radii of R1 and R2. (b) Calculated transmission using FDTD Solutions. (c)

Scanning electron microscope (SEM) image and (d) measured transmission of

the fabricated binary nanohole array for R1 ¼ 50 nm and R2 ¼ 110 nm.

FIG. 2. Phase maps of the electric field

of the binary nanohole array for a unit

cell at the plane across the centers of

each nanohole (Z¼ 15 nm) for (a)

ALCR mode and (b) ILCR mode.

Transmission of the binary nanohole

array for different R1, while R2 is fixed

at 110 nm extracted from (c) simula-

tions and (d) experiments. The bottom

row shows the corresponding SEMs of

the binary nanohole array.

171109-2 Zhao et al. Appl. Phys. Lett. 107, 171109 (2015)

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nanoholes can be regarded as electric dipoles collectively

oscillating with the incident light. The coupling effects

between neighboring nanoholes are relatively weak for the

field mainly concentrating inside each nanohole. When the

incident wavelength is 660 nm (Fig. 2(a)), the ALCR mode

is excited, and the nanoholes in the two arrays oscillate with

a phase difference of p. Because of the same strength of the

resonant amplitude, the reradiated fields of two arrays

strongly cancel each other out in the far field, and the cou-

pling between the structure and free space light is largely

minimized resulting in a Fano dip in transmission. At

740 nm (Fig. 2(b)), the ILCR mode dominates the radiation

with nanoholes in two arrays oscillating in the same phase;

thus, their reradiated fields interfere constructively and

strongly couple with the incident light.

The Fano profiles are closely related to the radius differ-

ence of the binary nanohole array. Figs. 2(c) and 2(d) show

the evolution of transmission spectra as R1 increasing from

40 nm to 110 nm, while R2 is fixed at 110 nm. As R1 gets

closer with R2, the Fano profile gradually diminishes, while

the resonance becomes much sharper with decreased line-

width and spectral contrast. Particularly, for the case of

R1 ¼ R2, the ALCR mode cannot be directly excited by nor-

mal incident light, and the Fano resonance disappears. To

more clearly observe the evolution of the resonance, the

spectral contrast defined as ðIpeak � IdipÞ=ðIpeak þ IdipÞ and

the Q factor is employed to measure the lineshape. The Q

factor defined by Q ¼ xa=2Wa can be calculated by fitting

the transmission spectra to the analytical model33

T ¼

x2 � x2a

2Waxaþ q

� �2

þ b

x2 � x2a

2Waxaþ q

� �2

þ 1

� a2

x2 � x2s

2Wsxsþ q

� �2

þ 1

; (1)

where x is the angular frequency of the incident field, xa

and xs are the resonant frequencies of Fano resonance and

superimposed Lorentz resonance, respectively. Wa and Ws

are the approximations of the spectral widths of both

resonances in frequency units. q and a are the asymmetry pa-

rameter and maximum amplitude of the resonance, respec-

tively. b is the modulation damping parameter originating

from intrinsic losses.33

Fig. 3 shows the evolution of Q factor and spectral con-

trast as R1 gets closer with R2, and the Q factor and spectral

contrast follow different evolution tendencies. As R1 increases,

the Q factor gradually increases (dark line in Fig. 3), indicating

the increasing energy density of the electric field stored in the

resonances of the system. However, the spectral contrast (red

line in Fig. 3) reaches its highest value at small R1 and

decreases as R1 gets larger. This is due to the fact that, in the

binary nanohole array with small radius difference, the energy

density of the electric field is much stronger, and a small loss

introduced by silicon and ITO can result in a large dissipation

of energy, which weakens the Fano profile and reduces the

spectral contrast. In other words, lower R1 means lower energy

density of the electric field stored in the resonance of the bi-

nary nanohole array as well as lower dissipation and higher

spectral contrast. The Q factors and spectral contrasts from

experimental results agree well with the calculations, and the

slight deviation is mainly due to the broadening of linewidth of

the resonances and stray light caused by fabrication defects

and imperfections. The ability of such structure to achieve

high Q factor while still maintaining relatively high spectral

contrast is especially beneficial to improve the performance of

the Fano resonance based devices.

In order to realize Fano resonance based optical modula-

tor, commercial nematic LC, E7, is chosen as the active

media due to its large birefringence (�0.2) and various

driven methods such as electrical field, acoustic wave, heat,

and light. For simplicity, here, we adopt the electric field to

drive the LC molecule realignment. The underlying tuning

mechanism is shown in Fig. 4(a), the binary nanohole array

and ITO glass form a LC cell. The LC molecules exhibit uni-

axial optical symmetry with two principal refractive indices

no and ne. The ordinary refractive index no is for the light

with electric field polarization perpendicular to the director

and the extraordinary refractive index ne is for the light with

electric field polarization parallel to the director. When no

voltage is applied, the rod-like LC molecules reside ran-

domly between the two ITO layers and form a domain struc-

ture, where LC molecules preferably align in the same

direction within one domain and vary randomly from domain

to domain. Macroscopically (in the scale much larger than

the domain size), the LC molecules can be characterized as

an effective media with average refractive index of na.

However, when a bias voltage is applied between the ITO

layer, electric dipoles are formed by one end of a molecule

having a net positive charge, while the other end has a net

negative charge. As a result, the dipole molecules tend to ori-

ent themselves along the direction of the field. Consequently,

the surrounding dielectric environment seen by the binary

nanohole array is actively controlled by the applied voltage.

The change in dielectric environment usually causes a shift

in resonance wavelength, thus, for a certain wavelength,

huge variation of transmission under different applied vol-

tages can be envisioned. In the simulations, the rod-like LC

molecules are modeled as an effective material with refrac-

tive index of n calculated with the help of the macroscopic

order parameter q1

n ¼ na �1

3Dnq; (2)

FIG. 3. Spectral contrast and Q factor evolution as R1 gets closer with R2.

171109-3 Zhao et al. Appl. Phys. Lett. 107, 171109 (2015)

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where na ¼ ð2no þ neÞ=3 is the average refractive index of

the unaligned LC and Dn ¼ ne � no is the LC birefringence

(ne ¼ 1:734 and no ¼ 1:525 for E7). By applying voltage,

the macroscopic order parameter changes from 0 (unaligned

sample) up to 1 (fully aligned state) and the effective refrac-

tive index varies from na to no, respectively.

Fig. 4(b) shows the simulated transmission spectra for

LC molecules under different macroscopic order parameter q(R1 ¼ 50 nm and R2 ¼ 110 nm). One can notice that the

incorporation of LC results in a sharp Fano profile with nar-

rower width, higher spectral contrast, and resonance wave-

length having a red shift due to the refractive index matching

of the dielectric media on both sides. As the LC molecules

tend to realign along the direction of the applied electrical

field, the effective refractive index seen by the binary nano-

hole array gradually decreases, resulting in a blue shift of the

profile. This is because the light field in the binary nanohole

array is dominated by its X and Y components, as the orien-

tation direction of the LC molecules rearrange from random

state to uniform state along the applied electric field; the

effective refractive index experiences a variation from na to

no. Fig. 4(c) shows the wavelength of the Fano peak for LC

molecules under different macroscopic order parameter q.

10 nm shift of resonance wavelength can be achieved with qchanging from 0 to 1, which is wider than the linewidth of

the Fano resonance.

To experimentally verify the numerical results, the LC

cell is prepared by forming the binary nanohole array with

ITO glass using a 31 lm spacer, and the infiltration process

is done under 80 �C in vacuum environment through capil-

lary action. After infiltration, the sample is slowly cooled

down to room temperature with air pressure recovered to

normal in order to push the LC molecules into the nanoholes.

Figs. 5(a) and 5(b) show the measured transmission spectra

of the binary nanohole array under different applied voltages.

The evolution of the spectra is in good agreement with our

theoretical analysis. The transmission dip blueshifts gradu-

ally from 722.5 nm to 713 nm as the applied voltage

increases, and 26.7 kV/cm voltage is enough to shift the reso-

nance from Fano peak to Fano dip. The Q factor keeps

almost unchanged with the variation of applied voltage (Fig.

5(c)). The maximum modulation depth of 85% is achieved at

713 nm as shown in Fig. 5(d). The transmission monoto-

nously decreases with the increased voltage, and the most

rapid change of transmission is for the applied voltage

around 10 kV/cm. At higher voltage, the variation saturates

FIG. 4. (a) Schematics of active con-

trol of the Fano resonance based opti-

cal modulator. E7 LC molecules

rearrange from random state to uni-

form state under an applied voltage.

(b) Transmission and (c) Fano peaks

for different macroscopic order param-

eter q (R1 ¼ 50 nm and R2 ¼ 110 nm).

FIG. 5. (a) Transmission of the binary nanohole array and (b) its partial

enlargement. (c) Q factors of the Fano resonance under different applied vol-

tages. (d) Transmission at the operating wavelength (713 nm) under different

applied voltages.

171109-4 Zhao et al. Appl. Phys. Lett. 107, 171109 (2015)

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because the nematic LC molecules are almost completely

aligned along the electric field.

In summary, the Fano resonance within a binary nano-

hole array composed of two nanohole arrays with different

radii are studied both numerically and experimentally.

Simulations using finite difference time domain method

demonstrate that the origin of such sharp resonance is from

the interaction of the hybridized ALCR mode and ILCR

mode. Measured transmission spectra agree very well with

the simulation results and show a different evolution tend-

ency of Q factor and spectral contrast against the radius dif-

ference of the two nanohole arrays. Taking advantage of the

easy tuning mechanism of E7 and the high Q factor and

spectral contrast of the resonance, such binary nanohole

array can act as a high performance optical modulator. The

transmission of the operating wavelength monotonously

decreases with the increasing applied voltage; an unprece-

dented modulation depth of 85% is achieved.

This work was supported by the National Natural

Science Foundation of China under Grant Nos. 50836002

and 51176041. The authors would like to thank the

assistance from the Laboratory of Microfabrication, Institute

of Physics, Chinese Academy of Sciences on the sample

fabrication.

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